In the interest of keeping calculations minimal, I suggest that the rate of recovery ought to be 1 hit point per level per day of rest. [EDIT: Bad idea. See comments.] Characters of 0 through 1st level would recover 1 hit point per day. A 9th level character would recover 9 hit points per day. The advantage, of course, is that all one needs to know is one's level. No calculations are required. The other advantage is that one is rewarded for one's level, which is a result of experience, rather than being rewarded for one's luck at rolling hit dice. [EDIT: True, but still a bad idea.]
I also suggest that the constitution bonus should be added to one's rate of hit point recovery. (Conversely, I do not recommend that the penalty for low constitution should be applied, on the the grounds that all characters should be guaranteed a minimum recovery rate of at least 1 hit point per day under normal circumstances.) It seems reasonable to me that the attribute representing one's health and endurance should be a contributing factor to one's ability to recover from injury. Those who are healthy recover more quickly than those who are not. [EDIT: I stand by that, but I haven't playtested it yet.]
So, in summary, my house rules for healing are:
Hit points are recovered at the rate of 1 hit point/level/day of rest.
- Any constitution bonus increases the rate of recovery accordingly.